偏微分方程半月坛学术报告(一):Formation of singularities for the relativistic Euler equations(I)

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:朱圣国
:2021-06-07 15:30
:厦大海韵园实验楼106报告厅

报告人:朱圣国(上海交通大学)

时  间:67日下午15:30-16:30

地  点:厦大海韵园实验楼106报告厅

内容摘要:

We consider large data problems for C1 solutions of the relativistic Euler equations. In the (1 + 1)-dimensional spacetime setting, if the initial data are strictly away from the vacuum, a key difficulty in considering the singularity formation is coming up with a way to obtain sharp enough control on the lower bound of the mass-energy density. For this reason, via an elaborate argument on a certain ODE inequality and introducing some key artificial (new) quantities, we provide one time-dependent lower bound of the mass-energy density of the (1+1)-dimensional relativistic Euler equations, which involves looking at the difference of the two Riemann invariants, along with certain weighted gradients of them. Ultimately, for C1 solutions with uniformly positive initial mass-energy density of the corresponding Cauchy problem, we give a necessary and sufficient condition for the singularity formation in finite time. This talk is mainly based on joint works with Nikolaos Athanasiou (ICL).

个人简介:

朱圣国,博士,上海交通大学数学科学学院副教授。入选2019年中组部国家海外高层次人才引进计划(青年项目)、2020年上海市海外高层次人才引进计划、2017年英国皇家学会“Newton International Fellow”2015年于上海交通大学获理学博士学位,曾先后在香港中文大学、澳大利亚莫纳什大学、英国牛津大学做博士后。主要从事与流体力学及相对论相关的非线性偏微分方程的理论研究工作,在可压缩Navier-Stokes Euler方程组的适定性和奇异性方面取得了一系列进展,论文发表在Arch. Ration. Mech. Anal.J. Math. Pures Appl.Ann. Inst. H. Poincare Anal. Non Lineaire等杂志。

 

联系人:王焰金